Finite Group Databasebeta

← #14759634

Subgroups — #14759634

Order 2816.

1320 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077834C211yesmaximal, characteristic
2C2×#10622758C211yesmaximal, characteristic, complemented
3C2×#10622757C211yesmaximal, characteristic, complemented
4#13077319C211yesmaximal, characteristic, complemented
5#13068943C211yesmaximal, characteristic, complemented
6#13068943C211yesmaximal, characteristic, complemented
7#13068918C211yesmaximal, characteristic, complemented
8#13068891C211yesmaximal, characteristic, complemented
9#13068891C211yesmaximal, characteristic, complemented
10#13068821C211yesmaximal, characteristic, complemented
11#13068560C211yesmaximal, characteristic, complemented
12#13068458C211yesmaximal, characteristic, complemented
13#13068451C211yesmaximal, characteristic, complemented
14#13068397C211yesmaximal, characteristic, complemented
15C2×C11×#568C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C11×#568—24no—
18C11×#568—24no—
19C2×C11×#131—21no—
20C2×C11×#131—21no—
21C2×C11×#131C2211yescharacteristic
22C2×C11×#131C2211yescharacteristic
23C2×C11×#131C2211yescharacteristic
24C2×C11×#131C2211yescharacteristic
25C22×C11×M16—21no—
26C22×C11×M16—21no—
27C22×C11×M16C2211yescharacteristic
28C22×C11×M16C2211yescharacteristic
29C2×#67003C2211yescharacteristic
30C2×#67003C2211yescharacteristic
31#10623322C2211yescharacteristic
32C2×#66954C2211yescharacteristic, complemented
33#10622852C411yescharacteristic, complemented
34#10622852C411yescharacteristic, complemented
35#10622851C411yescharacteristic, complemented
36#10622851C411yescharacteristic, complemented
37C2×#66901C2211yescharacteristic
38C2×#66901C2211yescharacteristic
39C2×#66901C2211yescharacteristic
40C2×#66901C2211yescharacteristic
41#10622846C2211yescharacteristic
42#10622846C2211yescharacteristic
43#10622841C411yescharacteristic, complemented
44#10622840C411yescharacteristic, complemented
45#10622831C411yescharacteristic, complemented
46#10622830C411yescharacteristic, complemented
47C4×C22⋊Dic11C2211yescharacteristic
48#10622820C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic
50#10622758—24no—
51#10622757—24no—
52C2×#66889C2211yescharacteristic, complemented
53C2×#66889C2211yescharacteristic, complemented
54#10622741—21no—
55#10622741—21no—
56#10622740—21no—
57#10622740—21no—
58C2×#66886C2211yescharacteristic, complemented
59C2×#66886C2211yescharacteristic, complemented
60#10622723C2211yescharacteristic, complemented
61#10622715C2211yescharacteristic, complemented
62#10622714C2211yescharacteristic, complemented
63C2×#66879C2211yescharacteristic, complemented
64C2×C8×Dic11C2211yescharacteristic, complemented
65#10622196C2211yescharacteristic, complemented
66#10622196C2211yescharacteristic, complemented
67#10622193C2211yescharacteristic, complemented
68#10622193C2211yescharacteristic, complemented
69#10622188C2211yescharacteristic, complemented
70#10622188C2211yescharacteristic, complemented
71C2×C11×#41—22no—
72C2×C11×#41—22no—
73C2×C11×#41—22no—
74C2×C11×#41—22no—
75C2×C11×#41—21no—
76C2×C11×#41—21no—
77C2×C11×#41C2×C411yescharacteristic
78C2×C11×#41C2×C411yescharacteristic
79C2×C11×#41C2311yescharacteristic
80C2×C11×#41C2311yescharacteristic
81C22×Q8×C11C2×C411yescharacteristic
82C22×D4×C11—21no—
83C22×D4×C11C2×C411yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11C2311yescharacteristic
86C2×#4339C2311yescharacteristic
87C11×#131—28no—
88C11×#131—28no—
89C11×#131—22no—
90C11×#131—22no—
91C11×#131—22no—
92C11×#131—22no—
93C11×#131—22no—
94C11×#131—22no—
95C11×#131D414yescomplemented
96C11×#131D414yescomplemented
97C2×C11×M16—28no—
98C2×C11×M16—28no—
99C2×C11×M16—21no—
100C2×C11×M16—22no—
101C2×C11×M16—22no—
102C2×C11×M16—21no—
103C2×C11×M16—21no—
104C2×C11×M16—21no—
105C2×C11×M16—21no—
106C2×C11×M16—22no—
107C2×C11×M16—22no—
108C2×C11×M16D411yescharacteristic
109C2×C11×M16D411yescharacteristic
110C2×C11×M16D411yescharacteristic
111C2×C11×M16D411yescharacteristic
112C2×C11×M16C2311yescharacteristic
113C2×C11×M16C2311yescharacteristic
114C22×C8×C11—21no—
115C22×C8×C11—21no—
116C22×C8×C11—21no—
117C22×C8×C11—21no—
118C22×C8×C11—21no—
119C22×C8×C11C2311yescharacteristic
120C22×C8×C11C2311yescharacteristic
121#67006—21no—
122C2×C22⋊Dic11—21no—
123#67003—22no—
124#67003—22no—
125#67003—22no—
126#67003—22no—
127C2×#4326C2×C411yescharacteristic
128C2×#4326C2×C411yescharacteristic
129C2×#4325C2×C411yescharacteristic
130C2×#4325C2×C411yescharacteristic
131C2×#4324C2×C411yescharacteristic
132C2×#4324C2×C411yescharacteristic
133C2×#4323C2×C411yescharacteristic
134C2×#4323C2×C411yescharacteristic
135#66983C2×C411yescharacteristic
136#66983C2×C411yescharacteristic
137#66982—21no—
138C4×C22⋊D11—21no—
139C4×C22⋊D11—21no—
140#66979C2311yescharacteristic
141#66977C2×C411yescharacteristic
142#66977C2×C411yescharacteristic
143C2×C4×Dic11C2311yescharacteristic
144C2×C4×Dic11C2311yescharacteristic
145C2×#4318C2311yescharacteristic
146C2×#4318C2311yescharacteristic
147C22×C11⋊C8C2311yescharacteristic
148C22×C11⋊C8C2311yescharacteristic
149#66954—22no—
150#66954—22no—
151C2×#4313—21no—
152C2×C8×D11—21no—
153#66901—22no—
154#66901—22no—
155#66901—22no—
156#66901—22no—
157#66899C2×C411yescharacteristic
158#66899C2×C411yescharacteristic
159#66899C2×C411yescharacteristic
160#66899C2×C411yescharacteristic
161#66896C2×C411yescharacteristic
162#66896C2×C411yescharacteristic
163#66896C2×C411yescharacteristic
164#66896C2×C411yescharacteristic
165C11⋊#95—21no—
166C22⋊(C11⋊C8)—21no—
167C22⋊(C11⋊C8)—21no—
168C22⋊(C11⋊C8)C2×C411yescharacteristic
169C22⋊(C11⋊C8)C2×C411yescharacteristic
170C22⋊(C11⋊C8)C2×C411yescharacteristic
171C22⋊(C11⋊C8)C2×C411yescharacteristic
172#66889—22no—
173#66889—22no—
174#66886—22no—
175#66886—22no—
176(C2×D11)⋊C8—21no—
177(C2×D11)⋊C8—21no—
178#66879—21no—
179#66879—22no—
180Dic11⋊C8—21no—
181Dic11⋊C8—21no—
182C8×Dic11—21no—
183C8×Dic11—22no—
184#21468—111nomaximal, Sylow
185C24×C11—21no—
186C24×C11#4111yescharacteristic
187C11×#41—24no—
188C11×#41—24no—
189C11×#41—24no—
190C11×#41—24no—
191C11×#41—22no—
192C11×#41—22no—
193C11×#41—22no—
194C11×#41—22no—
195C11×#41—21no—
196C11×#41—21no—
197C11×#41—21no—
198C11×#41—21no—
199C11×#41C2×D412yes—
200C11×#41C2×D412yes—
201C11×#41#4112yes—
202C11×#41#4112yes—
203C2×Q8×C11—22no—
204C2×Q8×C11—22no—
205C2×Q8×C11—21no—
206C2×Q8×C11C22×C411yescharacteristic
207C2×Q8×C11C22×C411yescharacteristic
208C2×D4×C11—24no—
209C2×D4×C11—24no—
210C2×D4×C11—21no—
211C2×D4×C11—21no—
212C2×D4×C11—21no—
213C2×D4×C11—21no—
214C2×D4×C11—22no—
215C2×D4×C11—22no—
216C2×D4×C11—21no—
217C2×D4×C11C22×C411yescharacteristic
218C2×D4×C11C22×C411yescharacteristic
219C22×C4×C11—24no—
220C22×C4×C11—24no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11C22×C411yescharacteristic
231C22×C4×C11C22×C411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11#4111yescharacteristic
235C22×C4×C11C2411yescharacteristic
236C2×C22⋊D11—21no—
237C2×C22⋊D11—21no—
238C2×C22⋊D11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241#4339—21no—
242#4339—21no—
243#4339—21no—
244#4339—21no—
245C2×D44C22×C411yescharacteristic
246C2×C4×D11—21no—
247C2×Dic22C22×C411yescharacteristic
248C11×M16—24no—
249C11×M16—24no—
250C11×M16—24no—
251C11×M16—22no—
252C11×M16—22no—
253C11×M16—24no—
254C11×M16—24no—
255C11×M16—22no—
256C11×M16—22no—
257C11×M16—21no—
258C11×M16—21no—
259C11×M16C2×D412yes—
260C11×M16C2×D412yes—
261C2×C8×C11—24no—
262C2×C8×C11—24no—
263C2×C8×C11—24no—
264C2×C8×C11—24no—
265C2×C8×C11—24no—
266C2×C8×C11—21no—
267C2×C8×C11—21no—
268C2×C8×C11—21no—
269C2×C8×C11—21no—
270C2×C8×C11C2×D411yescharacteristic
271C2×C8×C11C2×D411yescharacteristic
272C2×C8×C11C2×D411yescharacteristic
273C2×C8×C11C2×D412yes—
274C2×C8×C11C2×D411yescharacteristic
275C2×C8×C11C2×D412yes—
276C22⋊Dic11—21no—
277C22⋊Dic11—21no—
278C22⋊Dic11—21no—
279C22⋊Dic11—42no—
280#4326—22no—
281#4326—22no—
282#4325—22no—
283#4325—22no—
284#4324—22no—
285#4324—22no—
286#4323—22no—
287#4323—22no—
288(C2×D11)⋊C4—21no—
289(C2×D11)⋊C4—21no—
290C4⋊Dic11C22×C411yescharacteristic
291C4⋊Dic11C22×C411yescharacteristic
292Dic11⋊C4—21no—
293Dic11⋊C4—21no—
294C4×Dic11—21no—
295C4×Dic11—21no—
296C4×Dic11—21no—
297C4×Dic11—21no—
298C4×Dic11—21no—
299#4318—21no—
300#4318—21no—
301#4318—21no—
302#4318—21no—
303C2×C11⋊C8—21no—
304C2×C11⋊C8—21no—
305C2×C11⋊C8—21no—
306C2×C11⋊C8—21no—
307C2×C11⋊C8—21no—
308C2×C11⋊C8—21no—
309C2×C11⋊C8C22×C411yescharacteristic
310C2×C11⋊C8C22×C411yescharacteristic
311C2×C11⋊C8C22×C411yescharacteristic
312C2×C11⋊C8C22×C411yescharacteristic
313#4313—42no—
314C8×D11—42no—
315C2×#568D1111yescharacteristic, complemented
316#3002—111no—
317C2×#444—111no—
318C2×#443—111no—
319#2930—111no—
320#1876—111no—
321#1876—111no—
322#1871—111no—
323#1866—111no—
324#1866—111no—
325#1855—111no—
326#1789—111no—
327#1765—111no—
328#1764—111no—
329#1753—111no—
330C23×C11—24no—
331C23×C11—21no—
332C23×C11—21no—
333C23×C11—21no—
334C23×C11—21no—
335C23×C11—41no—
336C23×C11—41no—
337C23×C11—81no—
338C23×C11—81no—
339C23×C11C4×D411yescharacteristic
340C23×C11C4×D411yescharacteristic
341C23×C11C2×#4111yescharacteristic
342C22×D11—21no—
343Q8×C11—24no—
344Q8×C11—21no—
345Q8×C11—21no—
346Q8×C11C4×D412yes—
347Q8×C11C4×D412yes—
348D4×C11—24no—
349D4×C11—24no—
350D4×C11—24no—
351D4×C11—22no—
352D4×C11—22no—
353D4×C11—22no—
354D4×C11—22no—
355D4×C11—21no—
356D4×C11—21no—
357D4×C11C4×D412yes—
358D4×C11C4×D412yes—
359C2×C4×C11—24no—
360C2×C4×C11—24no—
361C2×C4×C11—24no—
362C2×C4×C11—21no—
363C2×C4×C11—21no—
364C2×C4×C11—21no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—21no—
368C2×C4×C11—21no—
369C2×C4×C11—21no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—21no—
373C2×C4×C11—21no—
374C2×C4×C11—21no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—21no—
378C2×C4×C11C4×D411yescharacteristic
379C2×C4×C11C4×D411yescharacteristic
380C2×C4×C11C23×C411yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C2×#4111yescharacteristic
385C2×C4×C11C2×#4111yescharacteristic
386C22⋊D11—41no—
387C22⋊D11—41no—
388C22⋊D11—81no—
389C22⋊D11—81no—
390C2×Dic11—22no—
391C2×Dic11—21no—
392C2×Dic11—21no—
393C2×Dic11—21no—
394C2×Dic11—41no—
395C2×Dic11—41no—
396C2×Dic11—41no—
397C2×Dic11—41no—
398C2×Dic11—41no—
399D44—21no—
400D44—21no—
401C4×D11—41no—
402C4×D11—41no—
403Dic22—21no—
404Dic22—21no—
405C8×C11—22no—
406C8×C11—22no—
407C8×C11—21no—
408C8×C11—21no—
409C8×C11#12012yes—
410C8×C11#12012yes—
411C11⋊C8—21no—
412C11⋊C8—21no—
413C11⋊C8—21no—
414C11⋊C8—21no—
415C11⋊C8—41no—
416C11⋊C8—41no—
417C22×#41C2×D1111yescharacteristic
418C2×#135—111no—
419C2×#135—111no—
420#568—24no—
421#568—24no—
422C2×#131—21no—
423C2×#131—21no—
424C2×#131—111no—
425C2×#131C2×D1111yescharacteristic
426C2×#131C2×D1111yescharacteristic
427C2×#131C2×D1111yescharacteristic
428C2×#131C2×D1111yescharacteristic
429C22×M16—21no—
430C22×M16—21no—
431C22×M16C2×D1111yescharacteristic
432C22×M16C2×D1111yescharacteristic
433#525—111no—
434#452—111no—
435#452—111no—
436#451—111no—
437#450—111no—
438#449—111no—
439#449—111no—
440#448—111no—
441#447—111no—
442#444—224no—
443#443—224no—
444#436—221no—
445#436—221no—
446#435—221no—
447#435—221no—
448C2×#108—111no—
449C2×#108—111no—
450#424—111no—
451C2×#104—111no—
452C2×#104—111no—
453C2×#104—111no—
454C2×#104—111no—
455C2×#104—111no—
456C2×#104—111no—
457#416—111no—
458#416—111no—
459#408—111no—
460#407—111no—
461C2×C22⋊C8—111no—
462#405—111no—
463C2×#97—111no—
464C2×C4×C8—111no—
465C4×C22⋊C4—111no—
466#341—111no—
467#341—111no—
468#339—111no—
469#339—111no—
470#336—111no—
471#336—111no—
472C22×C11—21no—
473C22×C11—21no—
474C22×C11—21no—
475C22×C11—21no—
476C22×C11—21no—
477C22×C11—21no—
478C22×C11—21no—
479C22×C11—21no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—41no—
483C22×C11—41no—
484C22×C11—41no—
485C22×C11—41no—
486C22×C11—81no—
487C22×C11—81no—
488C22×C11—84no—
489C22×C11C2×C4×D411yescharacteristic
490C22×C11#52511yescharacteristic
491C22×C11#52511yescharacteristic
492C2×D11—41no—
493C2×D11—41no—
494C2×D11—41no—
495C4×C11—21no—
496C4×C11—22no—
497C4×C11—22no—
498C4×C11—21no—
499C4×C11C2×C4×D411yescharacteristic
500C4×C11C2×C4×D411yescharacteristic
501C4×C11C2×#12011yescharacteristic
502C4×C11#52511yescharacteristic
503Dic11—42no—
504Dic11—41no—
505Dic11—41no—
506Dic11—41no—
507Dic11—81no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—21no—
513C2×#41—21no—
514C2×#41—111no—
515C2×#41C4×D1111yescharacteristic
516C2×#41C4×D1111yescharacteristic
517C2×#41C22×D1111yescharacteristic
518C2×#41C22×D1111yescharacteristic
519C22×Q8C4×D1111yescharacteristic
520C22×D4—21no—
521C22×D4C4×D1111yescharacteristic
522C23×C4—21no—
523C23×C4C22×D1111yescharacteristic
524#135—222no—
525#135—222no—
526#135—222no—
527#135—222no—
528C2×Q16—111no—
529C2×Q16—111no—
530C2×SD16—111no—
531C2×SD16—111no—
532C2×SD16—111no—
533C2×SD16—111no—
534C2×D8—111no—
535C2×D8—111no—
536#131—28no—
537#131—28no—
538#131—22no—
539#131—22no—
540#131—22no—
541#131—22no—
542#131—22no—
543#131—22no—
544#131—222no—
545#131—222no—
546#131C22⋊D1114yescomplemented
547#131C22⋊D1114yescomplemented
548C2×M16—28no—
549C2×M16—28no—
550C2×M16—21no—
551C2×M16—22no—
552C2×M16—22no—
553C2×M16—21no—
554C2×M16—21no—
555C2×M16—21no—
556C2×M16—21no—
557C2×M16—22no—
558C2×M16—22no—
559C2×M16—111no—
560C2×M16—111no—
561C2×M16—221no—
562C2×M16C22⋊D1111yescharacteristic
563C2×M16C22⋊D1111yescharacteristic
564C2×M16C22⋊D1111yescharacteristic
565C2×M16C22⋊D1111yescharacteristic
566C2×M16C22×D1111yescharacteristic
567C2×M16C22×D1111yescharacteristic
568C22×C8—21no—
569C22×C8—21no—
570C22×C8—21no—
571C22×C8—21no—
572C22×C8—21no—
573C22×C8—111no—
574C22×C8—111no—
575C22×C8—221no—
576C22×C8C22×D1111yescharacteristic
577C22×C8C22×D1111yescharacteristic
578#123—221no—
579C22⋊Q8—111no—
580C22⋊Q8—111no—
581#121—111no—
582#121—111no—
583#120—221no—
584C4×D4—221no—
585C4×D4—221no—
586#117—111no—
587C2×C22⋊C4—221no—
588C2×C42—111no—
589C2×C42—111no—
590#108—222no—
591#108—222no—
592C4⋊C8—221no—
593C4⋊C8—221no—
594#104—222no—
595#104—222no—
596#104—222no—
597#104—222no—
598#104—222no—
599#104—222no—
600#103—111no—
601#103—111no—
602#103—111no—
603#103—111no—
604#102—111no—
605#102—111no—
606#102—111no—
607#102—111no—
608C22⋊C8—111no—
609C22⋊C8—111no—
610C22⋊C8—111no—
611C22⋊C8—111no—
612C22⋊C8—221no—
613C22⋊C8—221no—
614C22⋊C8—221no—
615C22⋊C8—221no—
616#97—222no—
617#97—221no—
618C4×C8—222no—
619C4×C8—221no—
620#95—221no—
621C2×C11—21no—
622C2×C11—21no—
623C2×C11—41no—
624C2×C11—41no—
625C2×C11—42no—
626C2×C11—42no—
627C2×C11C4×#12011yescharacteristic
628C2×C11#295611yescharacteristic
629C2×C11#295711yescharacteristic
630D11—81no—
631C24—21no—
632C24#433911yescharacteristic
633#41—24no—
634#41—24no—
635#41—24no—
636#41—24no—
637#41—22no—
638#41—22no—
639#41—22no—
640#41—22no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—221no—
646#41—221no—
647#41—221no—
648#41—221no—
649#41#433912yes—
650#41#433912yes—
651#41C2×C22⋊D1112yes—
652#41C2×C22⋊D1112yes—
653C2×Q8—22no—
654C2×Q8—22no—
655C2×Q8—21no—
656C2×Q8—111no—
657C2×Q8C2×C4×D1111yescharacteristic
658C2×Q8C2×C4×D1111yescharacteristic
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—111no—
669C2×D4—221no—
670C2×D4—221no—
671C2×D4—221no—
672C2×D4C2×C4×D1111yescharacteristic
673C2×D4C2×C4×D1111yescharacteristic
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4C2×C4×D1111yescharacteristic
689C22×C4C2×C4×D1111yescharacteristic
690C22×C4#433911yescharacteristic
691C22×C4C2×C22⋊D1111yescharacteristic
692C22×C4C2×C22⋊D1111yescharacteristic
693C22×C4C23×D1111yescharacteristic
694Q16—222no—
695Q16—222no—
696SD16—222no—
697SD16—222no—
698SD16—222no—
699SD16—222no—
700D8—222no—
701D8—222no—
702M16—24no—
703M16—24no—
704M16—24no—
705M16—21no—
706M16—21no—
707M16—22no—
708M16—22no—
709M16—24no—
710M16—24no—
711M16—22no—
712M16—22no—
713M16—221no—
714M16—221no—
715M16—221no—
716M16—221no—
717M16—442no—
718M16C2×C22⋊D1112yes—
719M16C2×C22⋊D1112yes—
720C2×C8—24no—
721C2×C8—24no—
722C2×C8—24no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—24no—
728C2×C8—24no—
729C2×C8—111no—
730C2×C8—111no—
731C2×C8—111no—
732C2×C8—111no—
733C2×C8—221no—
734C2×C8—221no—
735C2×C8—221no—
736C2×C8—221no—
737C2×C8—221no—
738C2×C8—221no—
739C2×C8—442no—
740C2×C8C2×C22⋊D1111yescharacteristic
741C2×C8C2×C22⋊D1111yescharacteristic
742C2×C8C2×C22⋊D1112yes—
743C2×C8C2×C22⋊D1112yes—
744C2×C8C2×C22⋊D1111yescharacteristic
745C2×C8C2×C22⋊D1111yescharacteristic
746C4⋊C4—111no—
747C4⋊C4—111no—
748C4⋊C4—221no—
749C4⋊C4—221no—
750C22⋊C4—221no—
751C22⋊C4—221no—
752C22⋊C4—221no—
753C22⋊C4—221no—
754C22⋊C4—221no—
755C22⋊C4—442no—
756C42—221no—
757C42—221no—
758C42—221no—
759C42—221no—
760C42—221no—
761C11#2146811yescharacteristic, complemented, Sylow
762C23—24no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—41no—
768C23—41no—
769C23—81no—
770C23—81no—
771C23—221no—
772C23C4×C22⋊D1111yescharacteristic
773C23C4×C22⋊D1111yescharacteristic
774C23C2×#433911yescharacteristic
775Q8—24no—
776Q8—21no—
777Q8—21no—
778Q8—221no—
779Q8—221no—
780Q8C4×C22⋊D1112yes—
781Q8C4×C22⋊D1112yes—
782D4—24no—
783D4—24no—
784D4—24no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—21no—
790D4—21no—
791D4—221no—
792D4—221no—
793D4—441no—
794D4—441no—
795D4—881no—
796D4—881no—
797D4C4×C22⋊D1112yes—
798D4C4×C22⋊D1112yes—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—222no—
819C2×C4—221no—
820C2×C4—221no—
821C2×C4—221no—
822C2×C4—441no—
823C2×C4—441no—
824C2×C4—441no—
825C2×C4—441no—
826C2×C4—441no—
827C2×C4—441no—
828C2×C4—441no—
829C2×C4C4×C22⋊D1111yescharacteristic
830C2×C4C4×C22⋊D1111yescharacteristic
831C2×C4C22×C4×D1111yescharacteristic
832C2×C4C2×#433911yescharacteristic
833C2×C4C2×#433911yescharacteristic
834C2×C4C22×C22⋊D1111yescharacteristic
835C2×C4C22×C22⋊D1111yescharacteristic
836C2×C4C22×C22⋊D1111yescharacteristic
837C8—22no—
838C8—22no—
839C8—21no—
840C8—21no—
841C8—221no—
842C8—221no—
843C8—221no—
844C8—221no—
845C8—441no—
846C8—441no—
847C8#6700612yes—
848C8#6700612yes—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—22no—
854C22—22no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—81no—
864C22—81no—
865C22—84no—
866C22—441no—
867C22—441no—
868C22—441no—
869C22C2×C4×C22⋊D1111yescharacteristic
870C22#1062332211yescharacteristic
871C22#1062332211yescharacteristic
872C4—21no—
873C4—22no—
874C4—22no—
875C4—21no—
876C4—442no—
877C4—441no—
878C4—441no—
879C4—441no—
880C4—881no—
881C4C2×C4×C22⋊D1111yescharacteristic
882C4C2×C4×C22⋊D1111yescharacteristic
883C4#1062332211yescharacteristic
884C4C2×#6700611yescharacteristic
885C2—21no—
886C2—21no—
887C2—41no—
888C2—41no—
889C2—42no—
890C2—42no—
891C2—881no—
892C2C4×#6700611yescharacteristic
893C2#1307752311yescharacteristic
894C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#568C2
socleC22×C11C2×C4×D4
prime radical#13077834C2
cosocleC22×C4×C11C24
hypercenterC2×#568D11
hypocenterC11#21468
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ C2×#568

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#10622758C2semidirect
3. C2×#10622757C2semidirect
4. #13077319C2semidirect
5. #13068943C2semidirect
6. #13068943C2semidirect
7. #13068918C2semidirect
8. #13068891C2semidirect
9. #13068891C2semidirect
10. #13068821C2semidirect
11. #13068560C2semidirect
12. #13068458C2semidirect
13. #13068451C2semidirect
14. #13068397C2semidirect
15. C2×C11×#568C2semidirect
32. C2×#66954C22semidirect
33. #10622852C4semidirect
34. #10622852C4semidirect
35. #10622851C4semidirect
36. #10622851C4semidirect
43. #10622841C4semidirect
44. #10622840C4semidirect
45. #10622831C4semidirect
46. #10622830C4semidirect
52. C2×#66889C22semidirect
53. C2×#66889C22semidirect
58. C2×#66886C22semidirect
59. C2×#66886C22semidirect
60. #10622723C22semidirect
61. #10622715C22semidirect
62. #10622714C22semidirect
63. C2×#66879C22semidirect
64. C2×C8×Dic11C22semidirect
65. #10622196C22semidirect
66. #10622196C22semidirect
67. #10622193C22semidirect
68. #10622193C22semidirect
69. #10622188C22semidirect
70. #10622188C22semidirect
95. C11×#131D4semidirect
96. C11×#131D4semidirect
315. C2×#568D11semidirect
546. #131C22⋊D11semidirect
547. #131C22⋊D11semidirect
761. C11#21468semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130778342
C2×#106227582
C2×#106227572
#130773192
#130689432
#130689182
#130688912
#130688212
#130685602
#130684582
#130684512
#130683972
C2×C11×#5682
#2146811